OF ANATOMY AND PHYSIOLOGY

THE present communication is intended to illustrate results attained in the investigation of individual, racial, and specific variations of the astragalus by statistical methods, coupled with due regard to function and adaptation. For this purpose some data are here recorded which throw light on one particular set of variable features. The orientation of the calcaneum to the plane of the "ground" can be partly accomplished with the help of the long axis of the posterior surface, which makes an angle with the true vertical which varies greatly in different species, probably also in individuals.

most mammalian orders show differences in this respect. Within the Simiidae the differences are great; thus while the interval is generally wide in the Gorilla, the facets, as a rule, almost touch in the Orang-outan. In the Chimpanzee the interval scarcely exists, and in the Gibbons it is anteriorly almost obliterated, as is frequently the case in the Orang; whilst among the lower Primates, obliteration of the interval is found in the majority of cases.
In Simiidee, however, as in many other groups of mammals, there may be within a species great individual variation, and in the Gorilla the range appears to be wide (usually from 2-5 mm.). On the other hand, the range of variation is small in the Gibbon and Orang; each one of six Gibbons (of various species) showed approximation of facets, and among twelve Orangs, only two had an interval greater in width than 1-5 mm. (viz; 2 8).
Human races differ both in the average width of the interval and in the extent of its variation. As in Simiidse, greater variability is associated with greater mean width.
A series of nine pairs of astragali of aboriginal Australians showed uniformity in this feature, the interval being at its narrowest part 3-4 mm. wide; in some astragali of Veddas, Bushman, and Andamanese, on the other hand, there was almost complete approximation of the facets. Ancient Egyptians present great variation in this feature. In a series of 368 (Table IIA.) from the collection in the Cambridge University Museum, the width varied from 7 mm. down to complete obliteration. The width is relatively greater in large bones, while the interval is not usually apparent in children; these differences are indicated by the following data.
Of 109 large bones-in which the length (without os trigonum) measured at least 50 mrn.-27 per cent. had an interval over 5 mm. in width; of the remaining 259 (i.e. medium and small-sized bones) only 7-3 per cent. had an interval as great as 5 mm. in width (see also Section B (ii), " Lateral Height ").
On the other hand, the respective frequencies of specimens with narrow intervals (less than 2 mm.) were 9 per cent. and 8 per cent. A series of seventeen young astragali varying in length from 26 mm. to 44 mm. shows that as soon as ossification appears to be complete at this margin, the two facets are always approximated.
In Simiidae and man, the narrowest part of the interval is generally some distance posterior to the most dependent part of the external malleolar facet, and is bounded above by that part of the facet which articulates with the ligamentum talo-fibulare posterius videe infra). The condition is well seen in Cynocephalus, and fig. 2, No. 255, represents its occurrence in man. Less often in man, but frequently in Simiidae, the interval is even narrower at the apex than more posteriorly (as in Hylobates, Tables I. and III.), and in such cases the fibular facet has a sharp downwardly-directed apex.
Significance of the individual, racial, and generic differences of width of the interval.-The data discussed below treat the interval as an accidental quantity, depending both on the extent of the fibular facet and on the height of the lateral face, of the astragalus. These vary independently. There is some evidence that the magnitude of each dimension ultimately depends on an adaptation to the functions of the astragalus. In six English specimens specially dissected, the band was present for a short distance behind the apex of the process, and the interval was in no case very narrow. In a well-developed example it extends forwards round the apex of the fibular process and blends with the periosteum above the anterior slipping (if present) of the posterior calcanean facet; while backwards it extends beneath the attachment of the ligamentum talo-fibulare posterius, and blends with the hindmost and lower part of that ligament. The attachment of the middle and more constant part of the fibrous band to the periosteum is less close than it is at either extremity. Its superficial aspect is posteriorly in contact with (not blending with) the above-mentioned ligament. Further forward an extension of synovial membrane from the posterior calcaneo-astragalar joint typically separates it from ligaments talo-fibulare posterius and calcaneo-fibulare.
The grooved form of the interval, often seen just in front of the apex, is apparently for the lodgment of this fibrous band, rather than for the ligamentum talo-calcaneum laterale. Behind the apex the interval in the macerated bone is often ridged longitudinally. In the limb of a Kroo native which I examined, the fibrous band was well developed, but its contact with the ligamentum talo-fibulare posterius extended further forward than sometimes occurs in English specimens, owing to the small size of the upward synovial extension. Considerable lipping of the anterior margin of the posterior calcanean facet resulted in the synovial reflection passing high up on the astragalus in front of the apex.
In the Orang-outan there is usually neither slipping nor upward synovial extension. The Kroo native showed a resemblance to the Orang in the small development of the anterior limb of the attachment of the ligamentum talo-fibulare posterius.
A small representative of the fibrous band was found in a young Orang, and an indication of it may be sometimes seen in the human full-term foetus.
It also appears to be represented in Hylobates M4i1lleri.
The band is probably similar in nature to the fibrous thickenings found in association with the periosteum over parts of the pelvic and other bones. Indeed, there is usually a well-marked band on the astragalus extending backwards and inwards from the attachment of the ligamentum talo-fibulare posterius, between the trochlea and groove for M. flexor hallucis longus.
The band which occupies the interval, however, deserves mention on account of its variable bulk and length, and of its posterior attachment to the region of the os trigonum-even though man is only distantly related to mammals in whom that bone is normally a distinct entity. It may be called the " ligamentum laterale tali." Width of interval as a direct adaptation. -It cannot be said at present that any structure such as the fibrous band (ligamentum lateral tali) directly determines the width of the interval, since a facet easily undergoes extension. For example, the surface with which the external malleolar facet of the astragalus articulates is formed by the posterior fasciculus of the external lateral ligament (cartilage covered), in its lower and hinder portion, as well as by the fibula itself. A groove observed by Sewell to course forwards across the external malleolar facet in many Egyptian astragali, for a variable distance, is an indication of the position of the upper edge of the faceted ligament.
II. Variabilities in certain dimensions of the astragalus, and their significance (with Tables).-A number of features of the astragalus (therefore of fibula, tibia, and calcaneum) which influence the width of the nonarticular interval may be shown to present individual and racial variation in man, as well as differences in the mean type for the various Simiidaw.
The width of the " intervals" is obviously directly dependent on-(i) Vertical extent of external malleolar facet.
(ii) Height of fibular process of astragalus. In the various species of Primates and other mammalian orders, the mean value of each of these dimensions shows differences relatively both to the bulk of the animal and to the length of its limbs.
(i) The fibular articular facet on the astragalus is said to be more extensive vertically in the climbing animals,' than in those of other habit; and it is intelligible that the ankle-joint would gain in stability by such an arrangement, though it is also true that peculiar ligaments, such as the 1 E.g., see Prehistoric Man, by Duckworth (Cambridge), p. 38.
X-shaped external lateral ligament' of Ungulata and the Kangaroo, are sometimes developed to serve the requirements of stability. Evidence drawn from a comparison of the "Giant Primates" is equivocal. The depth of articulation2 (relatively to the length of the astragalus) is scarcely as great in the climbing Orang-outan as in the Chimpanzee and Gorilla, and far less than in man! But upon examination the standard of comparison, length of astragalus, is found open to suspicion. There is, in fact, good ground for the belief that the neck becomes longer in climbing animals, not only in relation to the whole astragalus, but to the " size " of the whole animal (for " Length of Neck and of Trochlear Facet, in various Mammalia," see (1) Volkov; and length of trochlear facet in Table II.). The neck has, indeed, become shorter in man and in those Simiidaw which (to a greater or lesser extent) adopt a bipedal mode of progression; on the other hand, it becomes of extraordinary length in certain of the lower Primates (Loris and Galago). Since the Orang-outan differs in this feature from its near relatives videe Table II.), the length of the astragalus (which is influenced by that of the neck) as a standard of comparison diminishes in value.

Standards of Comparison.
The length of the trochlear facet does not appear to show any correlation with habit of life; moreover, in the Simiidal and man, it is of fairly constant proportion to the general size of the animal. The hind limb (including the tibia) in the Gibbon and in man has become elongated, perhaps in relation to the erect attitude; consequently, the astragalus will in them appear disproportionately small if compared with the tibia. But allowance being made for this reduction in the two genera mentioned, it is found that the ratio of the lengths of trochlea and tibia are similar. The trochlear length is therefore a suitable3 as well as convenient standard of comparison (so far as present information goes) for the dimensions of the astragalus in " Giant Primates." If the depth of the fibular articulation be compared with the trochlear length, man is found associated with the Orang and Chimpanzee; the relative depth is rather smaller in the Gorilla.3 The ratio is probably 1 See Parsons, Journ. Anat. and Phys., vol. xxxiv., etc. 2 Measurements in Table I. were made from the apex to the upper border of the facet, parallel to its anterior border. 3 When measured, as here, along the axis of the facet, there is the drawback that the dimension is in man influenced by the development of a notch in the front of the trochlear facet. The notch is also well-marked in the Chimpanzee (and Cynocephalus), whereas it is scarcely to be seen in the Gorilla and Gibbon. There is, however, a considerable degree of correlation between the lengths of the trochlear facet and astragalus, since the " standard deviation " of the ratio is not more than about 02. small also in the Gibbon. It is possible that an increase of depth of the fibular articulation may be a characteristic adaptation to the erect attitude as well as to an arboreal mode of life.
Another interesting standard of comparison is the breadth of the trochlear facet, but available data are at present scanty. Measured in fifteen Egyptian astragali (at the level of the hinder end of the auricular facet), the ratio of the breadth to astragalar length varies from 45-'55 (average 483). Its correlation with the length of the trochlear facet is not close (ratio varies from *7 to *86, average -77), nor is the ratio with axial height close (-85 to 1P16, average 1P00). Astragali  Whatever be the factor responsible for these differences, the relative position of the Gibbon and Orang indicates that the amount of transmitted pressure is not the only influence. Moreover, if we consider the total articular width at the ankle-joint videe [1]), man is found to have the smallest ratio of breadth to length of either astragalus or trochlear facet.
If we use trochlear width (A) as a standard for comparison, a rough calculation (from the above figures and Table I.) of the relative depth of the fibular facet, man ( 91) is associated again with the Orang ( 90), in which it is smaller than in the Gibbon (Q95 ?), the Chimpanzee (1 -0), and the Gorilla (1'07). The ratio in a Cynocephalus was *77.
Hence the external malleolar facet is largest in man, whichever of the three standards of comparison be selected, and the proportion iLS similar in the Orang, except in regard to the abnormally great astragalar length. It is also noteworthy that the average ratios to astragalar length for the genera are very similar, but that individual variation is very great. For Egyptians the coefficient of correlation (NOY') is only *622 (calculated from 265 specimens).
Another point with regard to the height of the fibular facet requires note. The bones of the taller ancient Egyptians show a relatively smaller articular height than do those of lesser stature. This fact is scarcely in accord with the expectation of greater proportional strain on the stability of the ankle-joint in large people, owing to the greater increase of weight in proportion to their linear dimensions. The number of specimens on which the figures are based is, in this and all succeeding tables, indicated inside square brackets.
It is possible that ligamentous structures sustain the extra burden. Evidence in favour of this suggestion is found in the better development of the apex of the fibular malleolus in long fibule than in the shorter ones (in which the facet nearly reaches to the apex). Such development of the apex probably corresponds to high development of ligamentous structures, 1 About thirty English fibulae were examined.
Indeed, the whole of the fibular malleolus is more prominent in man than in the Gorilla.
In the series of Egyptian astragali, a small number were young bones, so the relatively large size of the facet in the smaller bones of the series may be indicative of the larger size in the young individual, since in a series of seventeen children (in which the astragalus has not completely ossified) the fibular facet is of unusual height, usually, indeed, closely approaching the posterior calcanean facet. Possibly, the greater height of the facet in small bones may be due to a sexual factor also.  (1). 2 The figure is too low, partly on account of the lack of ossification in some specimens at the hinder end.

Standard
Deviation.

3'6
The lengths here given have been measured without the os trigonum, i.e. from the posterior margin of the trochlear facet, on its axis, to the most distant point on the head (length " tr. ").
The axis of the trochlea is defined as the line drawn along the deepest part of the sagittal groove of the trochlear facet.
The lengths of a pair of astragali from the same individual have been bracketed together, just as occurs in the other tables.
(ii) Height of astragalus 'at fibular process (or "lateral height") varies from before backwards on account of the convexity of the trochlear margin above, and the concavity of the posterior calcanean facet below.
Measurements have been made obliquely upwards and forwards from the midpoint of the outer margin of the posterior calcanean facet to the point where a line through the apex of the facet (drawn parallel to the anterior border) cuts the upper border of the facet videe fig. 2). Some results are recorded in Table III.; this height is termed the lateral height (or " Ht. A").
The "lateral height" is measured approximately in the same plane as the axial height, and its magnitude depends partly on that height. If the transverse diameter of the trochlea slopes downwards and inwards, as in most Primates, the lateral height tends to be greater than the axial height. If, again, the short diameter of the posterior calcanean facet is inclined downwards and outwards, it also tends for this reason to be greater than the axial height. If the trochlear and posterior calcanean short diameters lie in parallel planes (which are sagittally horizontal), the lateral height is about equal to the axial height (as sometimes occurs in man). In short, if the planes meet externally (as is frequent in Primates) the angle between them (see section B, j3, " trochleo-calcanean angle ") is a determining factor in the lateral height (vide fig. 1).
The actual values of the "lateral height" (Table III.) indicate, in comparison with the dimensions given in Table I., how it comes about that the interval is so narrow in the Chimpanzee, but large in the Gorilla and big Egyptian. The individual variation found among Egyptians is accounted for by the moderate value of the correlation coefficient for lateral height, and height of facet, viz. '71 for 265 specimens.
Occasionally the height of the facet surpasses the "lateral height" in the human astragalus; the following figures show its greater incidence in smaller bones (compare incidence of narrow non-articular intervals, Section A): In these specimens the facet commonly shows a marked inferior extension at the apex. The relative size of the " lateral height" associates man with the Orang, whether the standard be length or width of trochlear facet; but the ratio to astragalar length shows progressive increase from the Orang through the Gorilla, which approaches man. The lateral height of the astragalus depends on the following two factorsa. Axial height (or "Ht. y"). It is in man a rough measure of the astragalar component of the posterior pier of the inner longitudinal arch of the foot. In man the dimension is characteristically large. Examination of its ratio to the length of the astragalus suggests that a progressive increase has occurred from the Orang-outan through the African Simiidae to Man.
If placed in comparison with the length of the trochlear facet (or with its width), man is again seen to present a contrast with the Orang (Table IV.).
There is no strong evidence of a difference in the relative height in the young Egyptian. In three young Orangs the height was below the limit of variation for ten adult specimens. Young specimens of Hylobates measured by Volkov, however, had a height at least as great as in the adult.
The range of variation in the Ancient Egyptian series, of the ratio to astragalar length, overlaps that in each genus of Simiidam which has been examined. The results obtained above may be corroborated and amplified by consideration of the greatest height of the trochlear axis, not above the posterior calcanean facet, but above the plane on which the astragalus rests (which may be termed " basal plane "). Its value may be inferred from Volkov's measurements of the height of the inner border of the trochlea above the basal plane, since in each of the genera the axis of the trochlear facet is on almost the same level as the inner border; the latter is slightly the lower in the Orang, while we find that in the Gibbon and man the axial basal height is slightly less than the internal height, which is here recorded as a ratio to the length of the trochlear facet. New-born European [4] .95 Peruvian d [11] .

101
The axial basal height (or in man, the internal height) is chiefly dependent on the two factors, axial height, and concavity of posterior calcanean facet. The above data for Simiidae indicate (taking into account the radius of curvature of the facet) that the axial height is considerably less than in man. The great difference shown to exist between certain human races is noteworthy, the " highest "-the Peruvian-exceeding the Negro by 10 per cent.
f3. Angle between lateral trochlear and posterior calcanean planes.--The short diameter of the posterior calcanean facet meets the long axis of the calcaneum at a nearly constant angle (about 600) in man, Simiidee, and many other Primates. Sagittally horizontal planes through the short diameters of the above facets meet at an angle, salient (usually) externally. It may be called the trochleo-calcanean angle.
This angle is in man (e.g., Ancient Egyptians) usually small, but may be as great as 200; occasionally the planes may be parallel, or they may even be inclined towards one another in the opposite direction, forming an angle salient internally (see Table VI.).
The Orang-outan and Gibbon resemble man in regard to this angle; but the angle in them tends to be more frequently negative than in man. On the other hand, in the Gorilla and Chimpanzee, as in lower Primates, the angle under discussion is usually at least a sixth of a right angle. I cannot at present provide statistical data. The great differences in the size of this angle are the obvious expression of the paradoxical association of the Orang-outan with man, ill respect of the great lateral height of the astragalus. The convergence of the planes being so accentuated in the Gorilla and Chimpanzee, the lateral height becomes smaller than the axial height, unlike man, and the other Simiidae. There is more convergence of the planes in man than in the orang, with the result that the lateral height in the former is (rela-tively to length of trochlear facet) very little more than in the latter, although the axial height is so much larger.
The trochleo-calcanean angle thus presents a second paradoxical association of Simia with the two bipedal genera, Homo and Hylobates (as has been noted above). It is obviously dependent on the inclination of each of the two planes bounding it, to the ground (or surface of support of the intact foot). The angle formed by each of these planes with the ground may be considered in turn, as follows: A. Coronal tibio-astragalar angle. B. Lateral angle of elevation of short axis of posterior calcanean facet. There is, apart from its dependence on these angles, no obvious physiological significance in the trochleo-calcanean angle.
The measurement of either of these angles requires the concurrent examination of the tibia or calcaneum. It still remains to be shown to what extent the upper part of the fibular facet of the astragalus may be employed as an indication of the vertical axis of tibia. It is probable that when the angle between the adjacent facets at the outer margin of the trochlea is much less than a right angle, there is present in the limb a small coronal tibio-astragalar angle, i.e. tilting inwards of the axis of the ankle-joint. One-sixth of the Egyptian series of astragali present a very " sharp margin "; and among these, bones of a small size predominate. From bones adjacent to the astragalus, however, some information as to these angles may be obtained.
A. Coronal tibio-astragalar angle.-In some determinations by Volkov of the " tibial angle," he measures this on the tibia between the coronal axis of the trochlear facet and the coronal plane, perpendicular to the long axis of the tibia. In all the Simiidaw the angle is of similar size, and measurements are given at 270 for the Gibbon, 250.3 for Chimpanzee, and 250.7 for Gorilla. Man presents a great contrast; the angle is in the Australian only 10.7, while in the European and Japanese it is averaged at 0°. The evolution of the horizontally disposed ankle-joint (viz., at right angles to tibial axis) from the oblique one would probably lessen the strain on structures uniting the leg-bones (especially the interosseous ligament), and would thus be a suitable adaptation when great weight became habitually transmitted through this joint, as occurs in man, and to a less extent in certain Simiidae.
The small angle of inclination in many lower Primates is in need of explanation. In a Semnopithecus entellus, for example, it was only 120 (Volkov), and in other genera it may be even less. The extent of inward or outward torsion of the tibia does not appear to be correlated with the tibiogastragalar angle.
,, B. The angle of elevation of the short axis of the posterior calcanean facet may be roughly estimated from examination of the corresponding facet of the associated calcaneum.
The orientation of the calcaneum to the plane of the "ground" can be partly accomplished with the help of the long axis of the posterior surface, which makes an angle with the true vertical which varies greatly in different species, probably also in individuals. Volkov terms this angle "torsion du talon," and gives data for members of various mammalian orders. In Simia it measures 160.5, in the In the ancient Egyptian series of calcanea, individual variation in the inclination of the facet on the calcaneum is considerable, but I cannot state its range. The angle of elevation sometimes measures about 200. Laidlaw states that, apart from its continuity with abnormal laterally disposed facets, the facet is not visible from the outer side of the calcaneum.
In the Gibbon and Orang-outan the inclination resembles that in man, but falls short of that found in a Gorilla and a Chimpanzee (where the amount of the slope reaches 300).
The great inward slope of the posterior facet of the calcaneum in the Gorilla and Chimpanzee would appear to render the joint less stable than in man. The development, as regards height and extent of the inner part of the posterior facet on the calcaneum in man, is associated with the assumption of the new function, viz., weight-transmission along the posterior pier of the inner longitudinal arch of the foot. Accompanying this there is diminution of importance of the more primitive function of this joint, that of pronation and supination of the foot (to which the great inward deviation of the head of the astragalus in the lower Primates is an adaptation, as pointed out by Elizabeth Clark).-The kind of movement at the joint has therefore changed from an extensive one with much vertical sagittal movement to one chiefly around an oblique axis through the region of the middle calcaneo-astragalar joint. The form of the posterior calcanean facet of the astragalus bears in man evidence of this change in (1) the lesser degree of concavity of the postero-Oaxternal border than at the medial angle of the facet (a corresponding feature for the calcaneum was noted by Laidlaw); (2) transverse flattening of the facet ;2 (3) the inward extent of the facet towards the sustentaculum tali whereby the hinder width of the facet becomes as great as the anterior width (instead of being posteriorly much smaller, as in all the Simniidae except the Orang); and, lastly (4) the nearly horizontal direction of the diameter perpendicular to its long axis.
There is an indication of the appearance of more than one of these human features in Hylobates. Beside the small angle of elevation of the facet, there is in small species transverse flattening out of the posterior portion of the facet; but I have not seen this latter feature in any specimens of the Orang or Baboon.
The paradoxical similarity of the Orang to the Gibbon and man in respect of the small trochleo-calcanean angle may now receive some explanation. It is probably dependent on the similar direction of the short axis of the posterior calcanean facet, viz., at a small degree of inclination to the horizontal (i.e. " ground ").
In man this axis is indeed more horizontal than in the two Simiidee, but the ankle-joint axis is also more horizontally disposed. The explanation of the great amount of inclination of the short axis of the posterior calcanean facet in the Gorilla and Chimpanzee is not clear, unless it be due to their probably recent acquisition of the occasional habit of walking on the soles-a habit which required an eversion of the foot, including the calcaneum.

SECTION C.-
Width of interval between fibular and posterior calcanean facets. The data discussed above throw light on the significance of its variation among Simiidae and in man. The distance between the trochlear axis and the posterior calcanean facet has been seen to show progressive increase from the Orang, through the Gorilla and Chimpanzee, to man. Owing to the larger trochleo-calcanean angle in the Gorilla than in the Orang-outan, however, the lateral height of the astragalus is scarcely as large as in the latter; this, however, does not result in a narrower " interval " in the Gorilla's astragalus than in the Orang, because the height of the fibular facet shows an enormous reduction, sufficient .to leave an interval much wider than in the Orang.
The trochleo-calcanean angle is small in man, less than in the Gorilla, so that the lateral height in man exceeds that in the Gorilla by much more than the difference of axial height (distance between trochlear and posterior calcanean facets). The interval, however, is no wider in man, because the fibular facet is of greater vertical extent in man than in the Gorilla.
Individual variations in man are due to variation in each of the dimensions-lateral height and height of facet. Evolution of such kind as to produce a human astragalus from one like that of the Gorilla has thus increased the axial height, has rendered the axes of the ankle-and posterior calcaneo-astragaloid joints more horizontal (with inward extension of the hinder part of the latter), and has increased the height of articulation with the fibular malleolus.
Since there apparently remains more scope for still further development in an extension of the malleolar facet, rather than in two axes which are already practically horizontal, it is probable that the "higher" type has a narrower interval.
The converse, however, is not necessarily true; and in the past history of man it is possible that the interval was never wider than it is on the average in modern races, owing to the simultaneous evolution of each of the four adaptations discussed above. Indeed, the interval is apparently narrow in the La Chapelle and Tilbury astragali; it is, however, wide in a Krapina astragalus (a cast of which is in the Cambridge Anatomical Museum).
Some Neolithic astragali, which Professor Keith has kindly placed at my disposal, present narrow intervals; and the same is true of the Gibraltar cave individual recently described by Dr Duckworth,' which is also ascribed to the Neolithic period. I hope shortly to present an account of the features of these ancient astragali, and to supplement the data here provided by a more extensive series of specimens derived from these and other genera of Primates: the small series from which the present conclusions are drawn are so inadequate that the suggestions can only be considered tentative.

SECTION D.
Orientation of the astragatus.-In the foregoing account the orientation of the astragalus has been assumed (except when the tibia and calcaneum were discussed) to be in reference to the " basal plane," viz., that on which the isolated astragalus rests. This plane is the one in reference to which Volkov's measurements in an extensive range of mammalian orders were carried out.
The astragalus does not occupy this position in the intact foot, either in Simiida or in man. The orientation to the "basal plane" effects a rotation partly in a vertical plane. In man the vertical plane is nearly sagittal in direction, while in the Gibbon the plane is nearer the coronal plane. The extent of the rotation is determined in very large part by the "depression of the head" (first measured by Virchow 2), and so far as present information goes, is of a similar order in the Gibbon, Gorilla, and man.
The difference between man and the Simiidae appears to be largely determined by the extent of the inward deviation of the neck, well known to be greater in the Simiidae than in man. The long axis of the posterior astragalar facet of the calcaneum is said by Laidlaw to present in ancient Egyptians an inclination to the horizontal which is remarkably constant, viz. 450, a statement which may prove useful in orientation.
Since between human races and individuals there are marked differences in the amount of the depression of the head, it is to be feared that estimates of the average difference between the true orientation and orientation in reference to the basal plane will not suffice alone for accurate orientation of the isolated astragalus in man.
So far as the present line of investigation has been carried, it justifies the hope that statistical treatment of the dimensions of a bone will assist in a study of adaptation to function.
Whereas the most paradoxical and unreal association of different species and genera occurs if measurements are made of dimensions which have little obvious relation to function, yet if dimensions are measured in relation to physiology, adaptation to function becomes apparent. The method is further justified by the characteristic deviations from the normal which are found in several dimensions of bones with some one abnormal feature. Such a feature is the accessory calcanean facet on the fibular process which was first described by Symington,' and again by Sewell (2). Some figures of dimensions of a series of Egyptian bones selected for well-marked accessory facets have been inserted in the tables to illustrate certain marked peculiarities.

MATERIAL.
Ancient Egyptians, the large series from which measurements have been provided, is composed of specimens from tombs: (1) Predynastic; (2) Dynastic to Ptolemaic and Roman period. The same series has been described by Sewell (2). Specimens of Simiidae and Australians and other races, in the Museum of the Royal College of Surgeons, London, as well as a series of undescribed Neolithic astragali, were kindly placed at my disposal by Professor Keith.
For specimens of six Gorillas, and for a pair from a Chimpanzee, I am indebted to Mr Pycraft, British Museum, South Kensington.
A second pair of Chimpanzee specimens and ten of the recorded 1 Symington, Journ. of Anat. and Phys., vol. xix. In fig. 2 are drawings of six astragali (Egyptian) selected for diversity in features which have here been considered.
Data relating to these astragali are given in the following Table (VI.), and may instructively be compared with the average values given in Tables  I.,   1 The numbers in brackets are measurements expressed as percentages of length of trochlear facet. 2 The numbers in brackets give separately, first, the angle presented by the posterior calcanean plane laterally with the basal plane (K); second, the angle similarly formed with that plane by the trochlear plane (T). an average depth of fibular facet, corresponds with a very narrow interval between the fibular and posterior calcanean facets. In No. 33c, although the axial height, y, of the astragalus is also 1Note on a Variable Feature of the Astragalus relatively very small, yet the mutual inclination of the trochlear and posterior calcanean facets is so little that the lateral height, A, is not remarkably small. On the other hand, the fibular facet is very shallow, so that the " interval " below it becomes unduly wide. In No. 687 the lateral height, A, is very large, resulting in a wide "interval," which is increased by a coincident shallowness of the fibular facet. A similar condition is found in No 255; but this bone is peculiar in that the axial height, y, is even greater than the lateral height, on account of the sharp inclination of the trochlear facet downwards and outwards.
No. 733 is of an enormous height, especially laterally (A), where it reaches the maximal value; so that although the fibular facet is of over average depth, the interval below is almost maximal.
In No. 727 we have a bone which axially is of nearly maximal height, but which has the posterior calcanean facet inclined so extraordinarily upwards and outwards that the lateral height (A) is less than the average value. This specimen is also illustrative of the way in which a very narrow interval may occur when shallowness of the astragalus (laterally) and depth of the fibular facet are both present in only a moderate, not an extreme, degree.
It is noteworthy that in six specimens not selected for absolute size, the two smallest ones had the " narrow interval "; this is illustrative of influence of the size factor.